In the literature of information theory, there is necessity for comparing the different measures of fuzzy entropy and this consequently, gives rise to the need for normalizing measures of fuzzy entropy. In this paper, we have discussed this need and hence developed some normalized measures of fuzzy entropy. It is also desirable to maximize entropy and to minimize directed divergence or distance...

Study of fuzzy entropy on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Built in uncertainty in IFSs, it is named as hesitance. It is contained in fuzzy membership function in itself by definition. Hence, designing fuzzy entropy is not easy because there is no general entropy definition about IFSs. By considering existing fuzzy entropy definitions, fuzzy entropy on IFSs is desig...

‎in this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by zou [operator inequalities associated with tsallis relative operator entropy‎, ‎{em math‎. ‎inequal‎. ‎appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and tsallis relative o...

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...

The fuzzy entropy h(T) of a dynamical system has been introduced in [5] (see also [1, 3, 8, 10]). Generalizing the notion of a fuzzy partition Mesiar and Rybarik have studied the p-entropy (see [7, 10, 11]) based on the Pap y-calculus ([9]). The notion is based on an increasing bijective function g : [0,oo] —> [0, oo], such that #(0) = 0 and #(1) = 1. The choice g(x) = x leads to the fuzzy entr...

Several types of entropy of fuzzy variables or fuzzy sets have been given in the literature in order to measure the degree of uncertainty. In order to measure the degree of uncertainty of fuzzy vectors, a new definition of entropy of fuzzy vectors is proposed. Some properties are then investigated and the relations between the entropy of fuzzy variables and fuzzy vectors are discussed.

Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a high-entropy secret into the same uniformly distributed key. A minimum condition for the security of the key is the hardness of guessing a value that is similar to the secret, because the fuzzy extractor converts such a guess to the key. We define fuzzy min-entropy to quantify this property of a noisy source of...

Similar to fuzzy set on a possibility space, uncertain set is a set-valued function on an uncertainty space, and attempts to model unsharp concepts. Entropy provides a quantitative measurement of the uncertainty associated with an uncertain set. This paper presents a formula for calculating the entropy of an uncertain set via its inverse membership function. Based on the formula, the entropy op...

Any physical or geometrical variation on a natural dynamical system should be identified by an observer. Also a method is required to compare different observers and evaluate their perspectives. Moreover complexity and/or uncertainty of the system should be measured through viewpoint of observers. In the approach presented in this paper an observer is identified mathematically by a function μ :...